Not sure if this is what you want to hear, but the Xbox is really only
useful as a Myth frontend. There's no way to get a capture device into
it, so recording TV with an Xbox is not possible.
Instructions on how to set up an Xbox as a frontend are on the wiki:
http://www.mythtv.org/wiki/index.php/Xbox_Frontend
Base requirements for a Myth backend are pretty modest, and with some
effort you can likely find a capable system for free or close to it. A
P3 700 is enough to run an SD setup, and machines stronger than this
are frequently doorstops these days. Have a look at freecycle.org --
you might get lucky.
However, you'll most likely have to spend some cash on a
hardware-encoding capture card (eg Hauppage PVR 150); you may need to
buy a capable video card (nvidia gf4 or better); you may need to boost
your RAM (256 will work, but you'll really want 512); and you'll need
a big HDD -- I wouldn't recommend anything less than 200 GB.
Good luck.
PS -- make sure you put in a subject next time -- messages without
subjects are often ignored.